The objective of this research is to provide applicable and informative statistical techniques for the evaluation of therapeutic trials and other experiments in the Health Sciences. This involves constructing methods for models whose infused structure will vary according to the kind of information available. Predictive sample reuse methods will be devised for censored data where low to moderate structure is assumed in the model. For high structure statistical paradigms, various predictive distributions of future observations conditioned on data of previous experiments will be derived. This will be informative in assessing therapies and predicting their effect on future subjects. Model selection procedures will be investigated to see how they affect prediction. Procedures for the detection and assessment of influential observations will be developed for various statistical paradigms applicable to problems of diagnosis, survival studies and functional relations among variables.